Each of the four submarines carries a sealed "letter of last resort" in the prime ministers hand, containing instructions to follow if the United Kingdom has been devastated by a nuclear strike.
He branded Mr Corbyn's opposition "juvenile" and "narcissistic" and said shadow cabinet members who voted against Trident should resign and return to the backbenches because they would be voting against Labour Party policy.
MPs in Worcestershire have defended their decision to help renew Trident last night - saying Britain's deterrent is "vital" in keeping people safe.
She noted that the developments on worldwide arena indicate that there is a continued race and endeavors made by several countries so as to own missiles and nuclear bombs.
Defence Secretary Michael Fallon told MPs Trident "puts doubts in the minds of our adversaries".
The 472 to 117 vote in the House of Commons last evening marked the first major victory for Theresa May as Prime Minister.
The head of the GMB trade union Tim Roache insisted Mr Corbyn should abide by existing Labour Party policy, which is to back Trident renewal.
Although preparatory work on renewal is already under way, Monday's vote gave the final green light to a new fleet of submarines which are due to come into service by the early 2030s.
The vote was called by new Prime Minister Theresa May, whose Conservative Party backed the motion, as did some Labour MPs.
The Catholic Bishops' Conference of England and Wales said in a statement ahead of the vote that they prayed that the decision taken by parliament would include the intention to "complete the elimination" of nuclear weapons.
She added: "As our Strategic Defence and Security Review (SDSR) made clear, there is a continuing risk of further proliferation of nuclear weapons".
Labour leader Jeremy Corbyn reiterated his opposition to the potential use of the weapons - one of the key elements of the doctrine of nuclear deterrence.
Asked directly whether she would authorise a strike which could kill 100,000 innocent people, she replied: "Yes".
He said if it was ever used it would "cause hundreds of thousands of civilian deaths", calling it a "weapon of mass destruction".
58 of Scotland's 59 MPs voted against Trident renewal - with Scotland's only Tory MP, David Mundell, being the sole supporter.
The submarines, based at Faslane on the River Clyde, carry up to eight Trident missiles, each capable of carrying several warheads.
After more than five hours of debate, MPs voted in favour of renewal by a majority of 355.